Effect of hyperinsulinaemia–hyperaminoacidaemia on leg muscle protein synthesis and breakdown: reassessment of the two-pool arterio-venous balance model

Abstract

Accurate measurement of muscle protein turnover is critical for understanding the physiological processes underlying muscle atrophy and hypertrophy. Several mathematical approaches, used in conjunction with a tracer amino acid infusion, have been described to derive protein synthesis and breakdown rates from a two-pool (artery–vein) model. Despite apparently common underlying principles, these approaches differ significantly (some seem to not take into account arterio-venous shunting of amino acids, which comprises ∼80–90% of amino acids appearing in the vein) and most do not specify how tracer enrichment (i.e. mole percent excess (MPE) or tracer-to-tracee ratio (TTR)) and amino acid concentration (i.e. unlabelled only or total labelled plus unlabelled) should be expressed, which could have a significant impact on the outcome when using stable isotope labelled tracers. We developed equations that avoid these uncertainties and used them to calculate leg phenylalanine (Phe) kinetics in subjects who received a [²H₅]Phe tracer infusion during postabsorptive conditions and during a hyperinsulinaemic–euglycaemic clamp with concomitant protein ingestion. These results were compared with those obtained by analysing the same data with previously reported equations. Only some of them computed the results correctly when used with MPE as the enrichment measure and total (tracer+tracee) Phe concentrations; errors up to several-fold in magnitude were noted when the same approaches were used in conjunction with TTR and/or unlabelled concentration only, or when using the other approaches (irrespective of how concentration and enrichment are expressed). Our newly developed equations should facilitate accurate calculation of protein synthesis and breakdown rates.

Key points

• Accurate measurements of muscle protein synthesis and breakdown rates are critical for understanding the processes underlying muscle atrophy and hypertrophy.

• Several mathematical approaches have been described to derive muscle protein synthesis and breakdown rates from a two-pool (artery–vein) model including metabolic tracers.

• We found that only some of the published approaches provide accurate protein turnover rates and only when the computations are made with mole percent excess as the measure of tracer enrichment and the sum of tracer and tracee as the corresponding concentration in the artery and vein; errors, up to several-fold in magnitude, result when computations are made with unlabelled concentration only, and/or enrichment expressed as tracer-to-tracee ratio or with any of the other equations (irrespective of how concentration and enrichment are expressed).

• Interpretation of muscle protein turnover rates and their validity requires careful attention to the mathematical approach used to calculate them.

Introduction

The arterio-venous (AV) blood sampling (AV balance) technique in conjunction with radioactive or stable isotope labelled amino acid tracer infusion and limb blood flow measurement has been extensively used to measure forearm and leg amino acid uptake and release rates as an index of muscle protein synthesis and breakdown rates under various physiological conditions (Nair et al. 1992; Newman et al. 1994; Tessari et al. 1996; Svanberg et al. 1999; Nielsen et al. 2002; Volpi et al. 2003; Sheffield-Moore et al. 2004; Holm et al. 2005; Katsanos et al. 2005; Pupim et al. 2005; Fujita et al. 2007; Wilkinson et al. 2007, 2013; Vesali et al. 2009; Gjedsted et al. 2011; Phillips et al. 2014; Andersen et al. 2015; Mallinson et al. 2015). The computational approach for this technique relies on a steady-state two-pool (artery and vein) model and the central premise that both labelled and unlabelled amino acids are taken up by the limb or shunted directly from the artery to the vein, whereas only unlabelled amino acids are released from the limb. Moreover, it is assumed that amino acids that are taken up by the limb are used for protein synthesis, whereas amino acids that are released into the vein in excess of those that are directly shunted from the artery are derived from protein breakdown. Thus, the measurement of protein synthesis with this approach requires the use of a tracer amino acid that is not metabolized in muscle (e.g. Phe) whereas protein breakdown can be measured with any amino acid that is not newly formed by the muscle (e.g. Phe or Leu).

Although conceptually simple, the actual analysis of AV balance data is quite complex when using stable isotope labelled tracers because, unlike radiolabelled tracers, stable isotope labelled tracers are not massless. Applying the AV principle with stable isotope labelled tracers therefore requires knowledge of the flux of both labelled and unlabelled amino acids into and out of the limb to properly account for the contribution of the tracer to protein synthesis and direct shunting from the artery into the vein. We have identified six different mathematical approaches (detailed in Supporting information) that were originally described by Barrett et al. (1987), Gelfand & Barrett (1987), Thompson et al. (1989), Bennet et al. (1990), Wolfe & Chinkes (2005) and Greenhaff et al. (2008), which have consistently been used to calculate protein synthesis and breakdown rates by various investigators (Nair et al. 1992; Newman et al. 1994; Tessari et al. 1996; Svanberg et al. 1999; Volpi et al. 2003; Sheffield-Moore et al. 2004; Holm et al. 2005; Katsanos et al. 2005; Pupim et al. 2005; Fujita et al. 2007; Wilkinson et al. 2007, 2013; Vesali et al. 2009; Gjedsted et al. 2011; Phillips et al. 2014; Andersen et al. 2015; Mallinson et al. 2015). Despite apparently common underlying principles, these approaches differ significantly, but the original reports often do not provide the exact underlying rationale or derivation for these diverse sets of equations. Moreover, only a few reports clearly specify the units of measurements required for the equations to be valid (e.g. whether enrichment is expressed as tracer-to-tracee ratio (TTR) or mole percent excess (MPE), or whether the concentration terms represent total (sum of labelled and unlabelled) or unlabelled amino acid only). Differences in the units of measurement could significantly affect the results and potentially lead to erroneous findings when stable isotope labelled tracers are used and the enrichment is sufficiently high.

The purpose of the present study was to evaluate and compare the accuracy and validity of the six previously published mathematical approaches (Barrett et al. 1987; Gelfand & Barrett, 1987; Thompson et al. 1989; Bennet et al. 1990; Wolfe & Chinkes, 2005; Greenhaff et al. 2008) and to demonstrate the magnitude of errors associated with these outcomes when using different units for concentrations and enrichments. We first determined leg protein synthesis and breakdown rates in 10 subjects who received a [²H₅]Phe infusion during basal, postabsorptive conditions and during a hyperinsulinaemic–euglycaemic clamp procedure (HECP) with concomitant whey protein ingestion by using a newly developed set of equations which clearly specify how enrichment and concentrations should be expressed, and explicitly account for AV shunting of amino acids. We used the HECP approach because the AV-balance method requires metabolic and isotopic steady state. We then calculated protein turnover rates by using the six previously described sets of equations (Barrett et al. 1987; Gelfand & Barrett, 1987; Thompson et al. 1989; Bennet et al. 1990; Wolfe & Chinkes, 2005; Greenhaff et al. 2008) in conjunction with both TTR and MPE as the unit of enrichment and/or total or only unlabelled Phe concentrations in the artery and vein, and compared these results to those obtained by using our newly developed set of equations. We used a Phe tracer because it is not metabolized or newly synthesized by muscle tissue; nevertheless, the principles described here apply to AV balance measurements with other amino acid tracers so long as they are not metabolized or their metabolic fate (e.g. oxidation of branched chain amino acids) is appropriately accounted for.

Methods

A subset of subjects (n = 10; age: 56.3 ± 4.4 years; BMI: 32.9 ± 2.4 kg m⁻², means ± SD) who participated in a study designed to evaluate the effect of protein ingestion on glucose and muscle protein kinetics (Smith et al. (2015) and unpublished data) participated in this protocol, which was approved by the Institutional Review Board of Washington University School of Medicine in St Louis, MO, USA. Written informed consent was obtained from all subjects before participation, and the study conformed to the Declaration of Helsinki.

Subjects were admitted to the Clinical Research Unit the night before the study. They consumed a standard dinner at ∼18.30 h and then fasted, except for water, until the next morning. At 06.00 h, a catheter was inserted into an arm vein for the infusion of insulin, dextrose and stable isotope labelled Phe; catheters for blood sampling were inserted (under local anaesthesia) into the radial artery of the opposite arm and in retrograde fashion into the femoral vein of one leg. At ∼06.45 h, a primed, constant infusion of [ring-²H₅]-l-Phe was started and maintained for 7 h (priming dose: 6.0 μmol (kg fat-free mass)⁻¹; infusion rate: 0.10 μmol (kg fat-free mass)⁻¹ min⁻¹); purchased from Cambridge Isotope Laboratories Inc., Andover, MA, USA). Four hours after the start of the Phe tracer infusion, the HECP was started and maintained for 3 h. Human insulin (Novolin R, Novo Nordisk, Princeton, NJ, USA) was infused at a rate of 50 mU (m² body surface area (BSA))⁻¹ min⁻¹ (initiated with a priming dose of 200 mU (m² BSA)⁻¹ min⁻¹ for 5 min and then 100 mU (m² BSA)⁻¹ min⁻¹ for an additional 5 min). Euglycaemia (blood glucose ∼100 mg dl⁻¹) was maintained by variable rate infusion of 20% dextrose (Baxter, Deerfield, IL, USA). During the 3 h HECP, subjects consumed a total of 0.45 g of whey protein (unflavoured Unjury®, ProSynthesis Laboratories, Inc., Reston, VA, USA) per kilogram fat-free mass (containing [ring-²H₅]Phe equivalent to 6% of the Phe content in whey protein to minimize changes in arterial plasma Phe enrichment during protein ingestion), dissolved in 360 ml water provided in small aliquots every 20 min. To adjust for the HECP-induced suppression of whole-body proteolysis, the [ring-²H₅]Phe infusion rate was reduced to 0.08 μmol (kg fat-free mass)⁻¹ min⁻¹ during the HECP. Arterial and femoral venous blood samples were obtained immediately before starting the tracer infusions and every 6–7 min during the last 20 min of the basal and HECP periods for AV balance measurement of protein synthesis and breakdown; additional arterial blood samples were obtained every 10 min during the clamp solely to monitor blood glucose concentration. Leg blood flow in the common femoral artery was measured between 120 and 180 min after starting the Phe tracer infusion (basal period) and between 60 and 180 min after starting the insulin infusion (clamp period) by using Doppler ultrasound (M-Turbo; Sonosite Inc., Bothell, WA, USA) and a linear array 13 to 6 MHz frequency probe (Sonosite Inc., Bothell, WA, USA).

Sample collection, processing and analyses

Blood samples were collected in chilled tubes containing heparin to determine glucose and insulin concentrations or EDTA to determine Phe concentration and enrichments. Samples were placed in ice and plasma was separated by centrifugation within 30 min of collection and then stored at −80°C until final analyses. Plasma glucose concentration was determined by using an automated glucose analyser (Yellow Spring Instruments Co, Yellow Springs, OH, USA). Plasma insulin concentration was measured by using a commercially available enzyme-linked immunosorbent assay (EMD Millipore, St Charles, MO, USA). Plasma Phe concentration and TTR were determined by using gas chromatography–mass spectrometry (GC-MS; MSD 5973 System, Hewlett-Packard) after adding a known amount of [1-¹³C]Phe to aliquots of each plasma sample and preparing the t-butyldimethylsilyl (t-BDMS) derivative of Phe (Smith et al. 2007). The concentration of unlabelled Phe was calculated from the m+0/m+1 ion ratio after calibration of the instrument response to standards of known concentration (i.e. 0 to 150 μm unlabelled Phe solutions spiked with a known amount of [1-¹³C]Phe). TTRs were measured by calibration of the instrument response (m+5/m+0 ion ratio) against a set of isotopic enrichment standards of known TTR (ranging from 0.0 to 0.2). When required for calculations, MPE was calculated as MPE = TTR/(1+TTR) ×100; the concentration of labelled Phe was calculated as unlabelled Phe concentration × TTR.

Calculations

Amino acid refers to the amino acid that is being traced; in the case of the present study, amino acid refers to Phe.

First, leg Phe kinetics were calculated by using the two-pool model outlined in Fig. 1 and the newly developed equations that explicitly track the flux of labelled and unlabelled Phe as described below. It is assumed that: (i) all of the Phe tracer removed from artery is used for protein synthesis, (ii) both labelled and unlabelled Phe are taken up by muscle and are shunted from the artery to the vein, (iii) protein breakdown releases only unlabelled Phe during the short duration infusion protocol, and (iv) the AV balance represents muscle protein metabolism with no contribution from other tissues (e.g. erythrocytes, fat, etc.).

Figure 1.

Two pool arterio-venous protein turnover model

Central principles to this model are that: (i) Phe uptake by the leg reflects Phe used for protein synthesis, (ii), labelled and unlabelled Phe are both taken up by the limb and shunted from the artery to the vein, (iii) only unlabelled Phe is released by the leg, and (iv) Phe appearance into the vein (other than Phe shunted from the artery) is release from protein breakdown. Abbreviations: A, artery/arterial; B, breakdown; C, concentration (in μm); F, flux rate (in μmol min⁻¹); L, labelled amino acid; PF, plasma flow rate (in l min⁻¹); S, synthesis; T, total amino acid (i.e. sum of labelled and unlabelled amino acid); TTR, tracer-to-tracee ratio; U, unlabelled amino acid; V, vein/venous.

Phe delivery to (via the artery) and outflow from (via the vein) the leg is the product of plasma concentration and flow rate using the Fick principle:

where FL, FU and FT represent the flux (μmol min⁻¹) of labelled, unlabelled and total Phe, respectively; the subscripts A and V represent artery and vein; CL, CU and CT represent the concentration (μm) of labelled, unlabelled, and total Phe, respectively; and PF is plasma flow rate (l min⁻¹) calculated from blood flow adjusted for haematocrit (Hct) (Smith et al. 2015). The rate of labelled Phe uptake by the leg for protein synthesis (FL_S) is derived from the AV balance of labelled Phe, and the uptake of unlabelled arterial Phe for protein synthesis (FU_S) is derived from this and the arterial TTR:

where TTR_A is the arterial tracer-to-tracee ratio (= CL_A/CU_A). Since no labelled Phe is released from protein breakdown, the flux of labelled Phe shunted from artery to vein (FL_shunt) equals the flux of labelled Phe leaving the vein. The flux of unlabelled Phe shunted is derived from this and the arterial TTR:

The percentage of Phe delivered to the leg via the artery that is shunted to the vein can be calculated by dividing FT_shunt by FT_A, and multiplying the quotient by 100; the percentage of Phe delivered to the leg via the artery that is taken up by the leg can be calculated as [1 – (FT_shunt/FT_A)] × 100.

Since no labelled Phe is released from protein breakdown, protein breakdown is calculated as the rate of unlabelled Phe into the vein minus the rate of unlabelled Phe shunted from the artery to the vein:

Finally, the AV net balance (NB) is:

where the subscripts L and U represent labelled and unlabelled Phe, respectively.

The following summary equations for net balance and total protein synthesis and breakdown can be derived from these basic flux relationships:

6

7

and

8

9

and

10

11

12

Note that eqns 6, 8 and 11 use total [sum of labelled (tracer) + unlabelled (tracee)] concentrations and MPE enrichments, and eqns 7, 9 and 12 use tracee (unlabelled) concentrations and TTR enrichments, providing users with flexibility.

Secondly, the leg Phe kinetics obtained by using our newly developed set of equations were compared to the leg Phe kinetics obtained by using the six sets of equations originally described by Barrett et al. (1987), Gelfand & Barrett (1987), Thompson et al. (1989), Bennett et al. (1990), Wolfe & Chinkes (2005) and Greenhaff et al. (2008), which are described in detail in the Supporting information. The equations presented by Barrett et al. (1987) were originally developed for use with radiolabelled tracers and were modified for use with stable-isotope labelled tracers as described by Nair et al. (1992). The equation presented by Barrett et al. (1987) to calculate protein breakdown includes contributions from arterial inflow, which was noted in the original paper, and an extraction ratio [(CL_A – CL_V) / CL_A] was presented that corrects for this. However, many subsequent investigators apparently have omitted the extraction ratio when calculating breakdown rates (Newman et al. 1994; Nielsen et al. 2002; Volpi et al. 2003; Fujita et al. 2007; Wilkinson et al. 2007, 2013; Gjedsted et al. 2011; Phillips et al. 2014). We therefore present leg Phe kinetics calculated both with and without the extraction ratio. In their book, Wolfe & Chinkes (2005) provide equations that use MPE and total (labelled plus unlabelled) concentration to calculate protein synthesis and breakdown rates as well as equations that use TTR and unlabelled concentration (to examine tracee only kinetics, which does not reflect actual rates of protein turnover when using a stable isotope labelled tracers that are not massless); they point out that when using the TTR approach, total protein synthesis rate can be obtained by multiplying the tracee only protein synthesis rate by (1 + TTR in arterial blood) and breakdown rate can be calculated by using total protein synthesis and total (sum or labelled and unlabelled) net balance. However, tracee only kinetics have apparently been used in their subsequent studies to describe actual (total) protein turnover rates (e.g. Katsanos et al. 2005). Thompson et al. (1989), Bennet et al. (1990) and Greenhaff et al. (2008) did not specify whether unlabelled or total concentration should be used. They used MPE in their description of the sample analysis, but these same equations have been used with enrichments expressed as TTR in other publications (Wolfe, 1992; Bell et al. 2005; Fujita et al. 2007). To examine the effect of varying the unit of measurement, we therefore calculated synthesis and breakdown rates using each of these sets of equations in conjunction with: (i) unlabelled Phe concentrations and MPE enrichments, (ii) unlabelled Phe concentrations and TTR enrichments, (iii) total (sum of labelled and unlabelled) Phe concentration and MPE enrichments, and (iv) total (sum of labelled and unlabelled) Phe concentration and TTR enrichments.

Statistical analyses

Student’s t test for paired samples was used to evaluate the effect the HECP with concomitant whey protein ingestion (HECP + Whey), compared to postabsorptive conditions, on glucose and insulin concentrations, plasma flow and leg Phe kinetics (calculated by using our newly, developed equations and the previously published ones). A P-value of ≤0.05 was considered statistically significant. Data are presented as means ± SEM. Statistical analyses were carried out with SPSS version 21 for Windows (IBM, Armonk, NY, USA).

Results

Plasma glucose and insulin concentrations and plasma flow

Arterial plasma glucose concentration was 93 ± 1 mg dl⁻¹ during postabsorptive conditions and 100 ± 1 mg dl⁻¹ during the HCEP+Whey; arterial plasma insulin concentration was 5 ± 1 μU ml⁻¹ during postabsorptive conditions and increased by ∼10-fold (to 56 ± 3 μU ml⁻¹) during the HECP+Whey (P < 0.01). Leg plasma flow was ∼155 ml min⁻¹ during postabsorptive conditions and increased by ∼25% (P < 0.01) during the HCEP+Whey (Table1).

Table 1.

Phe concentrations and enrichments in arterial and femoral venous plasma and leg plasma flow during postabsorptive conditions and during a hyperinsulinaemic–euglycaemic clamp procedure with concomitant whey protein ingestion

	Postabsorptive	HECP+Whey
Unlabelled (tracee) concentration (μm)
Arterial	59.3 ± 1.6	67.2 ± 1.8
Venous	64.5 ± 1.9	63.7 ± 1.9
Labelled (tracer) concentration (μm)
Arterial	7.2 ± 0.3	6.7 ± 0.4
Venous	6.1 ± 0.3	5.5 ± 0.3
Total (tracer + tracee) concentration (μm)
Arterial	66.5 ± 1.8	73.9 ± 2.1
Venous	70.5 ± 2.1	69.2 ± 2.1
AV concentration difference (μm)
Unlabelled	−5.2 ± 0.6	3.5 ± 0.6
Labelled	1.1 ± 0.1	1.2 ± 0.1
Total	−4.1 ± 0.5	4.7 ± 0.6
Tracer-to-tracee ratio (TTR)
Arterial	0.1208 ± 0.0046	0.0987 ± 0.0045
Venous	0.0940 ± 0.0032	0.0853 ± 0.0032
Mole percent excess (MPE; %)
Arterial	10.77 ± 0.37	8.97 ± 0.39
Venous	8.58 ± 0.27	7.85 ± 0.27
Plasma flow (l min−1)	0.155 ± 0.018	0.195 ± 0.021

Data are means ± SEM. HECP+Whey: hyperinsulinaemic–euglycaemic clamp procedure with concomitant whey protein ingestion.

Plasma Phe concentrations and enrichments

Phe concentrations (both labelled and unlabelled) and enrichments (expressed as TTR and MPE) in arterial and venous plasma are summarized in Table1. Total Phe concentration in the vein exceeded total Phe concentration in the artery by ∼6% during postabsorptive conditions; during the HECP+Whey, total Phe concentration in the artery increased by ∼10% (P < 0.001) whereas total Phe concentration in the vein did not change. Phe enrichment in the artery exceeded Phe enrichment in the vein by ∼20% and was slightly lower during the HECP+Whey than during postabsorptive conditions, both in the artery and the vein.

Leg phenylalanine kinetics derived by using our newly developed set of equations (Fig. 2)

Figure 2.

Leg phenylalanine kinetics during postabsorptive conditions (open bars) and during a hyperinsulinaemic–euglycaemic clamp procedure with concomitant whey protein ingestion (filled bars)

Hatched bars represent the difference between these two conditions. Data are means ± SEM. *Value significantly different from postabsorptive value (P < 0.05).

During postabsorptive conditions, 10.3 ± 1.2 μmol Phe (sum of labelled and unlabelled) per minute were delivered to the leg via the artery. Approximately 15% of the Phe delivered was taken up by the leg; the remaining ∼85% was shunted to the vein. The rate of Phe release from protein breakdown was 2.18 ± 0.24 μmol min⁻¹ and exceeded the rate of total Phe uptake by the leg (i.e. Phe used for protein synthesis: 1.55 ± 0.17 μmol min⁻¹) by ∼40%, resulting in a negative Phe AV net balance, indicative of net protein catabolism. During the HECP+Whey, total (sum of labelled and unlabelled) Phe delivery to the leg increased by ∼38% (to 14.3 ± 1.3 μmol min⁻¹, P < 0.001); the rate of Phe release from protein breakdown was suppressed by 27 ± 11% (P < 0.05) and the rate of Phe (sum of labelled and unlabelled) used for protein synthesis increased by 65 ± 12% (P < 0.001), resulting in a shift from net protein catabolism during postabsorptive conditions to a positive Phe AV net balance, indicative of net protein synthesis, during the HECP+Whey. The absolute changes in synthesis and breakdown (in μmol min⁻¹), and their relative contributions to the change in net balance, were not different (P = 0.68).

Comparison of leg Phe kinetics derived by using our data with the six previously described approaches

All previously published approaches (Barrett et al. 1987; Gelfand & Barrett, 1987; Thompson et al. 1989; Bennet et al. 1990; Wolfe & Chinkes, 2005; Greenhaff et al. 2008) describe the AV net balance as the difference between the Phe concentration in the artery and the vein multiplied by plasma flow. However, it is not always specified whether Phe concentration refers to total (labelled and unlabelled) Phe or only unlabelled Phe. The unlabelled Phe concentration difference between artery and vein was ∼25% less than the total Phe concentration difference, both during postabsorptive conditions and the HECP+Whey (Table1). Accordingly, the AV net balance calculated from the unlabelled Phe concentrations in the artery and the vein overestimated total net Phe release (protein breakdown) by ∼25% during postabsorptive conditions and underestimated total net Phe uptake (protein synthesis) by ∼25% during the HECP+Whey (Table2).

Table 2.

Comparison of leg phenylalanine kinetics derived by using individual subjects’ data summarized in Table1 and the newly proposed and six different previously published approaches

			Difference in mean values
			compared to mean values derived
	Condition		by newly developed equations
	Postabsorptive	HECP + Whey
	(μmol min−1)	(μmol min−1)	Postabsorptive	HECP+Whey
Net balance
(CTA – CTV) × PF	−0.63 ± 0.10	0.96 ± 0.20*	0.00 (0.0%)	0.00 (0.0%)
(CUA – CUV) × PF	−0.80 ± 0.12	0.74 ± 0.20*	−0.17 (26.5%)	−0.22 (−23.1%)
Phe release from protein breakdown
Newly developed equations	2.18 ± 0.24	1.47± 0.24*	—	—
Wolfe & Chinkes (2005)
Synthesis (MPE + CT) − Net balance (CT)	2.18 ± 0.24	1.47± 0.24*	0.00 (0.0%)	0.00 (0.0%)
Synthesis (MPE + CU) − Net balance (CU)	1.99 ± 0.22	1.35 ± 0.22*	−0.19 (−8.6%)	−0.12 (−8.0%)
Synthesis (TTR + CT) − Net balance (CT)	2.38 ± 0.27	1.59 ± 0.26*	0.20 (9.4%)	0.13 (8.7%)
Synthesis (TTR + CU) − Net balance (CU)	2.18 ± 0.24	1.47± 0.24*	0.00 (0.0%)	0.00 (0.0%)
Gelfand & Barrett (1987)
PF × CTV × [1 − (MPEV/MPEA)]	2.18 ± 0.24	1.47± 0.24*	0.00 (0.0%)	0.00 (0.0%)
PF × CUV × [1 − (MPEV/MPEA)]	1.99 ± 0.22	1.35 ± 0.22*	−0.19 (−8.6%)	−0.12 (−8.0%)
PF × CTV × [1 − (TTRV/TTRA)]	2.38 ± 0.27	1.59 ± 0.26*	0.20 (9.4%)	0.13 (8.7%)
PF × CUV × [1 − (TTRV/TTRA)]	2.18 ± 0.24	1.47± 0.24*	0.00 (0.0%)	0.00 (0.0%)
Barrett et al. (1987) with extraction ratio
{[(MPEA / MPEV) − 1] × CTA × PF} × [1 − (CLA − CLV)/CLA)]	2.18 ± 0.24	1.47± 0.24*	0.00 (0.0%)	0.00 (0.0%)
{[(MPEA / MPEV) − 1) × CUA × PF} × [1 − (CLA − CLV)/CLA)]	1.94 ± 0.21	1.33 ± 0.22*	−0.24 (−10.8%)	−0.14 (−9.4%)
{[(TTRA / TTRV) − 1] × CTA × PF} × [1 − (CLA − CLV)/CLA)]	2.44 ± 0.27	1.62 ± 0.27*	0.26 (12.2%)	0.15 (10.3%)
{[(TTRA / TTRV) − 1] × CUA × PF} × [1 − (CLA − CLV)/CLA)]	2.18 ± 0.24	1.47± 0.24*	0.00 (0.0%)	0.00 (0.0%)
Barrett et al. (1987) without extraction ratio, and Bennet et al. (1990) and Thompson et al. (1989)
[(MPEA / MPEV) − 1] × CTA × PF	2.58 ± 0.29	1.82 ± 0.31	0.40 (18.4%)	0.35 (24.0%)
[(MPEA / MPEV) − 1] × CUA × PF	2.30 ± 0.26	1.65 ± 0.28	0.12 (5.6%)	0.18 (12.3%)
[(TTRA / TTRV) − 1] × CTA × PF	2.89 ± 0.33	2.01 ± 0.34*	0.72 (32.8%)	0.54 (36.8%)
[(TTRA / TTRV) − 1] × CUA × PF	2.58 ± 0.29	1.82 ± 0.31	0.40 (18.4%)	0.35 (24.0%)
Greenhaff et al. (2008)
[(MPEA / MPEV) − 1] × CTV × PF	2.74 ± 0.32	1.71 ± 0.29*	0.57 (26.0%)	0.25 (16.9%)
[(MPEA / MPEV) − 1] × CUV × PF	2.51 ± 0.29	1.58 ± 0.27*	0.33 (15.1%)	0.11 (7.6%)
[(TTRA / TTRV) − 1] × CTV × PF	3.08 ± 0.36	1.89 ± 0.33*	0.90 (41.3%)	0.43 (29.0%)
[(TTRA / TTRV) − 1] × CUV × PF	2.81 ± 0.33	1.74 ± 0.30*	0.64 (29.2%)	0.27 (18.7%)
Phe used for protein synthesis
Newly developed equations	1.55 ± 0.17	2.43 ± 0.21*	—	—
Wolfe & Chinkes (2005)
(CTA × MPEA − CTV × MPEV) × (PF/ MPEA)	1.55 ± 0.17	2.43 ± 0.21*	0.00 (0.0%)	0.00 (0.0%)
(CUA × MPEA − CUV × MPEV) × (PF/ MPEA)	1.20 ± 0.13	2.09 ± 0.18*	−0.35 (−22.8%)	−0.34 (−14.0%)
(CTA × TTRA − CTV × TTRV) × (PF/ TTRA)	1.75 ± 0.19	2.55 ± 0.23*	0.20 (13.2%)	0.13 (5.3%)
(CUA × TTRA − CUV × TTRV) × (PF/ TTRA)	1.38 ± 0.15	2.21 ± 0.19*	−0.17 (−10.8%)	−0.22 (−9.1%)
Gelfand & Barrett (1987)
[(CLA − CLV)/CLA] × CTA × PF	1.55 ± 0.17	2.43 ± 0.21*	0.00 (0.0%)	0.00 (0.0%)
[(CLA − CLV)/CLA] × CUA × PF	1.38 ± 0.15	2.21 ± 0.19*	−0.17 (−10.8%)	−0.22 (−9.1%)
Barrett et al. (1987) with extraction ratio
Breakdown (MPE + CT) + Net Balance (CT)	1.55 ± 0.17	2.43 ± 0.21*	0.00 (0.0%)	0.00 (0.0%)
Breakdown (MPE + CU) + Net Balance (CU)	1.15 ± 0.13	2.07 ± 0.17*	−0.40 (−26.0%)	−0.36 (−14.8%)
Breakdown (TTR + CT) + Net Balance (CT)	1.81 ± 0.20	2.58 ± 0.23*	0.26 (17.1%)	0.15 (6.2%)
Breakdown (TTR + CU) + Net Balance (CU)	1.38 ± 0.15	2.21 ± 0.19*	−0.17 (−10.8%)	−0.22 (−9.1%)
Barrett et al. (1987) without extraction ratio and Bennet et al. (1990)
Breakdown (MPE + CT) + Net Balance (CT)	1.95 ± 0.22	2.78 ± 0.26*	0.40 (25.9%)	0.35 (14.5%)
Breakdown (MPE + CU) + Net Balance (CU)	1.50 ± 0.17	2.39 ± 0.22*	−0.04 (−2.9%)	−0.04 (−1.7%)
Breakdown (TTR + CT) + Net Balance (CT)	2.26 ± 0.25	2.97 ± 0.29*	0.72 (46.2%)	0.54 (22.2%)
Breakdown (TTR + CU) + Net Balance (CU)	1.78 ± 0.20	2.56 ± 0.24*	0.23 (15.2%)	0.14 (5.3%)
Thompson et al. (1989)
[(MPEA × CTA − MPEV × CTV) / MPEV] × PF	1.95 ± 0.22	2.78 ± 0.26*	0.40 (25.9%)	0.35 (14.5%)
[(MPEA × CUA − MPEV × CUV) / MPEV] × PF	1.50 ± 0.17	2.39 ± 0.22*	−0.04 (−2.9%)	−0.04 (−1.7%)
[(TTRA × CTA − TTRV × CTV) / TTRV] × PF	2.26 ± 0.25	2.97 ± 0.29*	0.72 (46.2%)	0.54 (22.2%)
[(TTRA × CUA − TTRV × CUV) / TTRV] × PF	1.78 ± 0.20	2.56 ± 0.24*	0.23 (15.2%)	0.14 (5.3%)
Greenhaff et al. (2008)**
[(MPEA / MPEV) – 1] × CTA – (CTA – CTV) × PF	17.57 ± 1.43	9.60 ± 1.94*	16.02 (1034%)	7.17 (296%)
[(MPEA / MPEV) – 1] × CUA – (CUA – CUV) × PF	15.89 ± 1.26	8.83 ± 1.75*	14.34 (925%)	6.40 (264%)
[(TTRA / TTRV) – 1] × CTA – (CTA – CTV) × PF	19.65 ± 1.65	10.70 ± 2.11*	18.10 (1168%)	8.27 (341%)
[(TTRA / TTRV) – 1] × CUA – (CUA – CUV) × PF	17.74 ± 1.45	9.82 ± 1.93*	16.19 (1045%)	7.40 (305%)

Data are means ± SEM. ^*Value significantly different from corresponding postabsorptive value (P < 0.05). ^**Synthesis rates calculated using the equation presented by Greenhaff et al. (2008) were ∼5- to 10-fold different from those derived by any of the other methods and therefore appear to be attributable to typos in the published equation. Abbreviations: CT, total (i.e. tracer and tracee) concentration; CT_A, total arterial concentration; CT_V, total venous concentration; CU, unlabelled (i.e. tracee) concentration; CU_A, unlabelled arterial concentration; CU_V, unlabelled venous concentration; CL_A, labelled arterial concentration; CL_V, labelled venous concentration; HECP+Whey, hyperinsulinaemic–euglycaemic clamp procedure with concomitant whey protein ingestion; MPE_A, mole percent excess in the artery; MPE_V, mole percent excess in the vein; PF, plasma flow; TTR_A, tracer-to-tracee ratio in the artery; TTR_V, tracer-to-tracee ratio in the vein. Leg phenylalanine kinetics were calculated by using the arterial concentrations and enrichments obtained during the AV balance study described in the methods section. The equations presented by Barrett et al. (1987) and Gelfand & Barrett (1987) were originally described for radioactive tracers and have been adapted for use with stable isotope labelled tracers as described by Nair et al. (1992) (i.e. total and labelled Phe concentrations in the artery and vein and enrichments expressed as MPE). Furthermore, Barrett et al. (1987) present a commonly used equation to calculate protein breakdown that includes contribution from arterial inflow as well as an extraction ratio that corrects for this; therefore, we present breakdown rates for Barrett et al. (1987) using both approaches.

The rates of Phe used for protein synthesis varied from 1.15 to 2.26 μmol min⁻¹ during postabsorptive conditions and from 2.07 to 2.97 μmol min⁻¹ during HECP+Whey, the rate of Phe released from protein breakdown varied from 1.94 to 3.08 μmol min⁻¹ during postabsorptive conditions and from 1.33 to 2.01 μmol min⁻¹ during HECP+Whey (Table2). The extent to which Phe used for protein synthesis was stimulated and Phe release from protein breakdown was suppressed during the HECP+Whey (compared to postabsorptive conditions) varied by ∼2-fold and up to ∼60%, respectively (Fig. 3) amongst the different approaches.

Figure 3.

Change (from postabsorptive conditions) in Phe utilization for protein synthesis (filled bars) and release from protein breakdown (open bars) during the hyperinsulinaemic–euglycaemic clamp procedure with concomitant whey protein ingestion calculated by using individual subjects’ data summarized in Table 1 and the newly proposed and six different previously published approaches

Phe turnover rates for Barrett et al. (1987) were calculated two ways: (i) protein breakdown as initially presented in their methods section, and (ii) with an extraction ratio applied that corrects for the contribution from arterial inflow. Changes in the synthesis rates for Greenhaff et al. (2008) were calculated for the purposes of this figure as the difference between net balance and breakdown because the rates calculated using the equations presented in the original paper result in synthesis rates that are ∼5- to 10-fold different from those derived by any of the other methods and therefore appear to be attributable to errors in the reported formula. Data are percentage change from postpabsorptive values ± SEM of the change. Abbreviations: CT, total (i.e. tracer and tracee) concentration; CU, unlabelled (i.e. tracee) concentration; ER, extraction ratio; MPE, mole percent excess; TTR, tracer-to-tracee ratio.

Only a few previously published approaches consistently resulted in synthesis and breakdown rates that matched those obtained with our newly developed set of equations, namely those described by Barrett et al. (1987), when the extraction ratio [(CL_A – CL_V) / CL_A] was applied to their breakdown equation, Gelfand & Barrett (1987), and Wolfe & Chinkes (2005) when used in conjunction with total Phe concentrations and MPE enrichments. The same sets of equations (Barrett et al. 1987; Gelfand & Barrett, 1987; Wolfe & Chinkes, 2005) used in conjunction with unlabelled Phe concentrations and MPE as enrichments and total or unlabelled Phe concentrations and TTR as enrichments resulted in significant errors in either the rate of Phe used for protein synthesis (up to ∼25%) or Phe released from protein breakdown (up to ∼10%), or both, although Wolfe & Chinkes (2005) point out that when using TTR as the enrichment and unlabelled concentrations, total synthesis rates can be obtained by multiplying the result by (1 + TTR in arterial blood).

The equations described by Barrett et al. (1987) without the extraction ratio applied, Thompson et al. (1989), and Bennet et al. (1990) resulted in significant errors in the rates of both Phe used for protein synthesis (up to ∼45%) and Phe released from protein breakdown (up to ∼40%), irrespective of the concentration and enrichment measurement units used. Synthesis rates calculated by using the equation presented by Greenhaff et al. (2008) were ∼5- to 10-fold different from those derived by any of the other methods and therefore appear to be attributable to errors in the reported equation. In addition, while all approaches resulted in a statistically significant HECP+Whey-induced increase in synthesis rate, a statistically significant decrease in protein breakdown was not identified by some approaches (Table2).

Discussion

There is ongoing debate about the relative contributions of protein synthesis and breakdown to muscle growth and atrophy-inducing stimuli (Phillips & McGlory, 2014; Reid et al. 2014), which cannot be solved until muscle protein synthesis and breakdown rates are consistently measured correctly in people. To help resolve this issue, we used a constant [²H₅]Phe tracer infusion in conjunction with the AV-balance approach to measure muscle protein synthesis and breakdown rates during postabsorptive conditions and during physiologically relevant (el-Khoury et al. 1995; Carey et al. 2003; Munsters & Saris, 2012; Saad et al. 2012; Kiskini et al. 2013) increases in plasma insulin and amino acid concentrations (HECP+Whey). We then mathematically described the flux of both tracer and tracee from the artery into the muscle, from the muscle into the artery and from the artery into the vein and used these data to present two sets of final equations to be used with either total (sum of tracer and tracee) concentration in conjunction with MPE, or tracee (unlabelled) concentration in conjunction with TTR in arterial and venous plasma to accurately measure protein synthesis and breakdown rates. This approach takes into account the fact that stable isotope labelled tracers (unlike radioactive tracers) are not massless. We compared these results with those obtained using the same data and previously published equations (Barrett et al. 1987; Gelfand & Barrett, 1987; Thompson et al. 1989; Bennet et al. 1990; Wolfe & Chinkes, 2005; Greenhaff et al. 2008) that are frequently used (Nair et al. 1992; Newman et al. 1994; Tessari et al. 1996; Svanberg et al. 1999; Volpi et al. 2003; Sheffield-Moore et al. 2004; Holm et al. 2005; Katsanos et al. 2005; Pupim et al. 2005; Fujita et al. 2007; Wilkinson et al. 2007, 2013; Vesali et al. 2009; Gjedsted et al. 2011; Phillips et al. 2014; Andersen et al. 2015; Mallinson et al. 2015). We found that: (i) only a small portion of amino acids delivered to the leg via the artery is taken up by the leg; the majority (∼80–90%) is shunted to the vein; (ii) during postabsorptive conditions the rate of muscle protein breakdown exceeded the rate of muscle protein synthesis by ∼40%, (iii) during HECP+Whey, the rate of muscle protein synthesis increased by ∼65% and the rate of muscle protein breakdown decreased by ∼27%; however, (iv) the absolute HECP+Whey-induced changes (expressed in μmol min⁻¹) in breakdown and synthesis were not different and both synthesis and breakdown contributed equally to the HECP+Whey-induced increase in net balance. Previously published (Barrett et al. 1987; Gelfand & Barrett, 1987; Thompson et al. 1989; Bennet et al. 1990; Wolfe & Chinkes, 2005; Greenhaff et al. 2008) and frequently used (Nair et al. 1992; Newman et al. 1994; Tessari et al. 1996; Svanberg et al. 1999; Volpi et al. 2003; Sheffield-Moore et al. 2004; Holm et al. 2005; Katsanos et al. 2005; Pupim et al. 2005; Fujita et al. 2007; Wilkinson et al. 2007, 2013; Vesali et al. 2009; Gjedsted et al. 2011; Phillips et al. 2014; Andersen et al. 2015; Mallinson et al. 2015) approaches often yielded discrepant results, which was due to failure to account for AV shunting of amino acids (as outlined in the Supporting information) and/or not taking into account that stable isotope labelled tracers are not massless and therefore contribute directly to the total amount of amino acids used for protein synthesis.

The equations described by Barrett et al. (1987) when adapted for stable isotope labelled tracers according to Nair et al. (1992) and including the extraction ratio [i.e. (CL_A – CL_V) / CL_A)] to adjust the calculated breakdown rate, and the equations described by Wolfe & Chinkes (2005) and Gelfand & Barrett (1987) can be used to accurately calculate rates of protein synthesis and breakdown as long as enrichments are expressed as MPE and total (tracer plus tracee) concentrations are used. When computed with unlabelled (tracee) concentrations in the artery and vein or TTRs as the measure of enrichment, the error for total synthesis rate and in some cases also breakdown can range from a few per cent to several-fold. The equations described by Barrett et al. (1987), Wolfe & Chinkes (2005) and Gelfand & Barrett (1987) yield accurate protein breakdown rates even if used in conjunction with enrichments expressed as TTR and unlabelled concentrations because this approach computes tracee flux only, and unlike protein synthesis, which incorporates both tracer and tracee into muscle protein, protein breakdown reflects only the release of unlabelled (tracee) Phe into the vein. Wolfe & Chinkes (2005) in their book also point out that their equation used with TTR and unlabelled concentrations yields tracee only kinetics, which can be converted to total turnover rates by multiplying the tracee only protein synthesis rate by (1 + TTR in arterial blood). However, tracee only kinetics have apparently been used in their subsequent studies to describe actual (total) protein turnover rates (e.g. Katsanos et al. 2005).

Accordingly, the use of TTR vs. MPE in these equations is not right or wrong; both, if applied correctly can give valid results and help discern tracee kinetics only vs. kinetics of the total (tracee + tracer) system. In order to obtain the desired results, however, it is important to match the enrichment measurement unit with the corresponding concentration measurement unit (i.e. TTR with unlabelled only concentration and MPE or APE with total concentration). In addition, we contend that, if the goal is to measure protein synthesis and breakdown rates, a common definition of these parameters has to be adhered to (i.e. protein synthesis refers to the process of building protein from amino acids and protein breakdown refers to the process of breaking down protein into individual amino acids) and only total (tracee + tracer) turnover rates are valid.

The equations described by Barrett et al. (1987) without the extraction ratio to adjust the breakdown rate, Thompson et al. (1989), Bennet et al. (1990), and Greenhaff et al. (2008) computed synthesis and breakdown rates incorrectly, irrespective of how enrichment and concentrations were expressed, and yielded not only quantitatively incorrect results but would have also affected the conclusions from our study. The HECP+Whey-induced suppression of protein breakdown failed to achieve statistical significance when calculated using the equations by Barrett et al. (1987) without the extraction ratio applied, Thompson et al. (1989) or Bennet et al. (1990), when enrichment was expressed as MPE irrespective of whether unlabelled or total concentrations were used and when enrichment was expressed as TTR and unlabelled concentrations were used because these approaches slightly underestimated the actual extent to which protein breakdown was suppressed (by ∼15%) and yielded greater sample variance (i.e. a ∼20–30% larger SD than with our equations). Problems with the conceptual framework for the equations described by Bennet et al. (1990) and Thompson et al. (1989) have previously been noted by Wolfe & Chinkes (2005); nevertheless, these equations (and derivations of them) have continued to be frequently used (Fujita et al. 2007; Gjedsted et al. 2011; Wilkinson et al. 2013; Phillips et al. 2014). Part of the inaccuracy of this approach stems from the fact that AV shunting of tracer and tracee is not appropriately accounted for, which leads to an overestimation of Phe released into the vein from protein breakdown. A correction factor (an extraction ratio calculated as [(labelled concentration in the artery – labelled concentration in the vein) divided by labelled concentration in the artery] has been proposed by Barrett et al. (1987) to help resolve this issue. Applying this correction factor to the equations described by Bennet et al. (1990) and Thompson et al. (1989) results in accurate synthesis and breakdown rates when used in combination with enrichments expressed as MPE and total Phe concentrations, but not when used with TTR and unlabelled Phe concentration.

These findings highlight the need to carefully consider the analytical approaches used to obtain amino acid concentration and enrichments to study amino acid/protein kinetics. An HPLC-based amino acid analyser system yields total (tracer plus tracee) concentration whereas measurement of amino acid concentration by inclusion of a stable isotope labelled internal standard and isotope dilution mass spectrometry will typically measure only the tracee (unlabelled) amino acid concentration. Isotopic enrichment is typically expressed as either TTR or MPE, but the results are interconvertable [MPE = TTR/(1 + TTR) × 100, and TTR = MPE/(1 − MPE)] / 100. Our newly developed equations should facilitate accurate calculation of protein synthesis and breakdown rates regardless of how the data were obtained. There are, nonetheless, some limitations to our approach. First, it cannot overcome the assumptions that are inherent to the two-pool AV balance approach, i.e. that all Phe taken up by the tissue is used for protein synthesis and does not accumulate in the intracellular compartment, and that all Phe derived from protein breakdown is released into the vein. While outside the scope of the present manuscript, a three-pool model that incorporates measurement of the concentration and enrichment of intracellular free amino acids has been proposed to help resolve some of these concerns (Biolo et al. 1995). Importantly, however, the same principles discussed here (i.e. calculating the flux of both labelled and unlabelled Phe into and out of each compartment) apply to any such model.

In conclusion, the validity of reported protein synthesis and breakdown rates obtained by using the AV-balance technique depends on the mathematical approach used. Some approaches can correctly describe rates of uptake and release by the leg (i.e. those described by Barrett et al. (1987) when the extraction ratio is applied to their breakdown equation, Gelfand & Barrett (1987), and Wolfe & Chinkes (2005)), but the accuracy of the results is exquisitely sensitive to the concentration (labelled plus unlabelled vs. unlabelled only) and enrichment (TTR vs. MPE) measurement units used, whereas others (those described by Barrett et al. (1987) without the extraction ratio applied to the breakdown equation, Thompson et al. (1989), Bennet et al. (1990), and Greenhaff et al. (2008)) do not compute synthesis and breakdown rates correctly regardless of measurement units used and can result in up to several-fold errors. The results from these studies therefore need to be interpreted with caution. Our newly developed set of equations that fully accounts for AV shunting of amino acids and explicitly state the required units of measurements should facilitate accurate calculation of protein synthesis, breakdown, and net balance.

Glossary

A

artery

AV

arterio-venous

BMI

body mass index

BSA

body surface area

CL

labelled amino acid concentration

CT

total (sum of labelled and unlabelled) amino acid concentration

CU

unlabelled amino acid concentration

FL_S

rate of labelled amino acid uptake by the leg for protein synthesis

FL_shunt

flux of labelled amino acid shunted from artery to vein

FU_B

rate of unlabelled amino acid released into the vein from protein breakdown

FU_S

rate of unlabelled amino acid uptake by the leg for protein synthesis

FU_shunt

flux of unlabelled amino acid shunted from artery to vein

FT_S

rate of total (sum of labelled and unlabelled) amino acid uptake by the leg for protein synthesis

FT_shunt

flux of total (sum of labelled and unlabelled) amino acid shunted from artery to vein

GCMS

gas chromatography–mass spectrometry

Hct

haematocrit

HECP

hyperinsulinaemic–euglycaemic clamp procedure

MPE

mole percent excess

NB_L

labelled amino acid arterio-venous net balance

NB_T

total (sum of labelled and unlabelled) amino acid arterio-venous net balance

NB_U

unlabelled amino acid arterio-venous net balance

Phe

phenylalanine

PF

plasma flow rate

t-BDMS

t-butyldimethylsilyl

TTR

tracer-to-tracee ratio

V

vein

Additional information

Competing interests

The authors have no competing interests.

Author contributions

G.I.S. conducted the metabolic studies, assisted in processing study samples, collected data, performed the data analyses, and drafted the manuscript. B.W.P. developed the new equations and edited the manuscript. S.J.K. was responsible for arterio-venous catheterization and medical supervision. B.M. designed the study, obtained funding for the study, was involved in conducting the metabolic studies, processing study samples, collecting data, developing the new equations and performing the data analyses, and finalized the manuscript.

Funding

This publication was made possible by NIH grants DK 94483, DK 56341 (Washington University School of Medicine Nutrition and Obesity Research Center), DK 020579 (Washington University School of Medicine Diabetes Research Center), GM 103422 (Washington University School of Medicine Biomedical Mass Spectrometry Resource) and UL1 TR000448 (Washington University School of Medicine Clinical Translational Science Award) including KL2 sub-award TR 000450.